This Seeking Tech guide will explain how you can download the free Dark Beginnings DLC for Sonic X Shadow Generations. This prologue is only available for the PS4 and PS5 versions.
For the first step, open the PlayStation Store and then search for Sonic.
Afterwards, open the Sonic X Shadow Generations product page.
You should then be able to find the Dark Beginnings DLC when you scroll down to the Add-Ons section.
After downloading and installing the DLC, you will be able to watch the prologue from the Shadow Generation section of the game.